Step 1: Split the puzzle into three separate shapes.
Instead of looking at the whole picture together, look at the oval, the first triangle, and the second triangle one at a time.
Each candidate piece must complete all three shapes together, so checking them one by one narrows down the choice fast.
Step 2: Trace the oval alone.
Cover everything except the oval's visible edge and the curved patch in each option.
Only a patch with a small, gentle curve of the right size keeps the oval looking like a smooth, closed oval, not a circle or a flat shape, and this already rules out S, since its curved patch is far too large.
Step 3: Trace the first triangle alone.
Look only at the cut corner of the triangle at the top of the main figure.
The missing piece needs a small triangular corner tilted at the same angle to close this triangle without a kink, and Q's triangle corner tilts the wrong way, so Q is ruled out at this step.
Step 4: Trace the second triangle alone.
Now look only at the triangle shown just below the box in the main figure.
The missing piece needs a lower triangle with a matching slant to close this second triangle, and R's lower triangle has a different slant, so R is ruled out here.
Step 5: Confirm the surviving option.
After removing S, Q, and R for failing one shape each, only P is left.
P's curve, its top triangle corner, and its lower triangle all match the three shapes in the main figure at the same time.
Final Answer:
Checking the oval and both triangles one at a time leaves only P as the piece that fits.
\[ \boxed{\text{P}} \]